In a trunk optical transmission system there is a need to store high-speed client signals economically, and transmit huge volumes of information. As part of the process to achieve this objective, from the standpoint of improving the frequency utilization efficiency, a digital coherent transmission method which employs a combination of coherent detection and digital signal processing is being investigated, and it is anticipated that it will be possible to achieve high-speed, high-volume information transmissions by means of wavelength division multiplexing using the aforementioned transmission method. In this transmission method, carrier phase synchronization is established via digital signal processing. In consideration of the circuit scale and modulation format, various types of algorithms and packaging methods are being investigated for the structure of the carrier phase synchronization circuit (CPR: Carrier Phase Recovery).
In contrast, in an optical transmission system in which coherent detection is utilized, because amplitude and amplitude information are used, such a system is conspicuously affected by phase noise (i.e., noise in the phase direction). Main sources of such phase noise include phase noise arising from the line width of the lasers used in the transmission and receiving terminals, frequency offset caused by the frequency of the lasers used in the transmission and receiving terminals, and phase noise arising from a non-linear optical effect. For example, the Viterbi-Viterbi algorithm (see Non-patent document 1) is one algorithm for performing carrier phase synchronization blindly on the receiving side.
FIG. 38 is a block diagram showing the structure of a carrier phase synchronization circuit (CPR) that utilizes the Viterbi-Viterbi algorithm. Here, a description is given of when QPSK (Quadrature Phase Shift Keying) is used as the modulation format. In this case, M corresponds to 4. The input symbols are shown as complex values having an in-phase component I and a quadrature component Q.
This CPR is formed by a carrier phase estimation unit 150 and a carrier phase compensation unit 160. The carrier phase estimation unit 150 is formed by an M-power circuit 151, an averaging circuit 152, an angle calculation circuit 153, an unwrapping circuit (not shown), a divider circuit 154, and a complex number calculation circuit 155. The carrier phase compensation unit 160 is provided with a delay circuit 161 and a multiplier circuit 162.
The input symbols that are input sequentially into the CPR are shown by the following Formula (1).[Formula 1]rk=Akexp(jθk+φk)+wk  (1)
Here, k is the time, sk=Akexp(jθk) is the transmission symbol, wk is the additive noise, and φk is the phase noise. In the Viterbi-Viterbi algorithm, by assuming an M-PSK (M-ary Phase Shift Keying) for the modulation technique, the fact that Ak is constant and θk is expressed as 2πmk/M is utilized. Note that mk is an integer between 0 and M−1.
The input symbol rk is input into the M-power circuit 151 and the delay circuit 161. The M-power circuit 151 raises the input symbol to the M-th power. As a result of this M-power operation on the input symbol, when wk≈0, the output is as is shown in Formula (2).
                    (                  Formula          ⁢                                          ⁢          2                )                                                                                                                r                k                M                            =                            ⁢                                                A                  k                  M                                ⁢                                  exp                  ⁡                                      (                                                                  j                        ⁢                                                                                                  ⁢                        M                        ⁢                                                                                                  ⁢                                                  θ                          k                                                                    +                                              j                        ⁢                                                                                                  ⁢                        M                        ⁢                                                                                                  ⁢                                                  ϕ                          k                                                                                      )                                                                                                                          =                            ⁢                                                A                  k                  M                                ⁢                                  exp                  ⁡                                      (                                                                  j2π                        ⁢                                                                                                  ⁢                                                  m                          k                                                                    +                                              j                        ⁢                                                                                                  ⁢                        M                        ⁢                                                                                                  ⁢                                                  ϕ                          k                                                                                      )                                                                                                                          =                            ⁢                                                A                  k                  M                                ⁢                                  exp                  ⁡                                      (                                          j                      ⁢                                                                                          ⁢                      M                      ⁢                                                                                          ⁢                                              ϕ                        k                                                              )                                                                                                          (        2        )            
In actual fact, because wk≠0, the output from the M-power circuit 151 is input into the averaging circuit 152, and the effects of noise are reduced. The averaging circuit 152 obtains an average, for example, by adding up the M-power values of the input symbols calculated by the M-power circuit 151 on a complex plane for every L number of averaged window widths which include the M-power values of the previous and subsequent input symbols, and thereby reduces the noise components. Next, the output from the averaging circuit 152 is input into the angle calculation circuit 153.
The angle calculation circuit 153 calculates the angle of deviation of the symbols (i.e., complex numbers) that have been averaged by the averaging circuit 152. If the noise has been sufficiently reduced by the averaging circuit 152, then the output from the angle calculation circuit 153 is Mφk. In this calculation method, the symbols are converted into an angle by, for example, calculating in-phase components (I) and quadrature components (Q) in the output from the averaging circuit 152, and then calculating the arctan (Q/I). The unwrapping circuit corrects the arbitrariness (360°×n, wherein n is an integer) remaining in the angle calculated by the angle calculation circuit 153. Specifically, the unwrapping circuit corrects the angle such that the difference between the angle for the immediately prior input symbol and the current angle is reduced.
The divider circuit 154 calculates carrier phase estimation values by multiplying by (1/M) the angle that was corrected by the unwrapping circuit. The complex number calculation circuit 155 calculates a size 1 complex number in order to make the carrier phase estimation value calculated by the divider circuit 154 into an angle of deviation, and outputs this to the multiplier circuit 162.
The delay circuit 161 attaches to an input symbol a delay for the time required for the calculations from the M-power circuit 154 to the complex number calculation circuit 155, and outputs the input symbol to the multiplier circuit 162 at the same timing as it outputs the size 1 complex number which corresponds to that particular input symbol. The multiplier circuit 162 multiplies the input symbol to which a delay was attached by the delay circuit 161 by the complex number calculated by the complex number calculation circuit 155, and synchronizes the result with the carrier phase of the input symbol.